EBK SYSTEM DYNAMICS
3rd Edition
ISBN: 9780100254961
Author: Palm
Publisher: YUZU
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Chapter 2, Problem 2.56P
To determine
To prove:
The final value theorem
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Q1.Given the unity feedback system with a forward path transfer function,
G(s) =
=
K
(s+1)(s+2)(s+6)
. Do the following:
(a) Draw the root locus
(b) Find the gain, K, and natural frequency for a damping ratio 0.5.
(c) Find the range or value of gain, K for
i. overdamped ii. critically damped iii. Undamped iv. underdamped
Q. 1: The partial Routh array of a unity feedback system is given below.
S6
1
Adel
8
S5
1
S4
2
Bash
6
-4
0
C
0
How many roots does it have in the right half plane? Comment on the
stability of the system. Determine the characteristic equation of the system.
Q.2: Find the values of Ki and K2 for the system shown in the figure below
when Mp=0.25% and tp= 4 sec. assume unit step input.
R(S)
K₁
C(S)
1+ K₂S
Temperature
EXAMPLE 1: A diesel engine is fitted with a turbocharger,
which comprises a radial compressor driven by a radial
exhaust gas turbine. The air is drawn into the compressor at
a pressure of 0.95 bar and at a temperature of 15°C, and
is delivered to the engine at a pressure of 2.0 bar. The
engine is operating on a gravimetric air/fuel ratio of 18: 1,
and the exhaust leaves the engine at a temperature of
600°C and at a pressure of 1.8 bar; the turbine exhausts at
1.05 bar. The isentropic efficiencies of the compressor and T(K)
turbine are 70 per cent and 80 per cent, respectively.
Calculate (i) the temperature of the air leaving the
compressor (ii) the temperature of the gases leaving the
turbine (iii) the mechanical power loss in the turbocharger
expressed as a percentage of the power generated in the
turbine. Using the values of : Cpair = 1.01 kJ/kg K, Vair = 1.4
Cpex = 1.15 kJ/kg K, Yex = 1.33
and
2s
с
P2
Engine
P3
W
W₁ = mexpex (T3-TA)
At
W₁ = mair Cpex
(T2-T₁)
4
P4…
Chapter 2 Solutions
EBK SYSTEM DYNAMICS
Ch. 2 - Prob. 2.1PCh. 2 - Solve each of the following problems by direct...Ch. 2 - Solve each of the following problems by separation...Ch. 2 - Prob. 2.4PCh. 2 - Prob. 2.5PCh. 2 - Obtain the Laplace transform of the following...Ch. 2 - Obtain the Laplace transform of the function shown...Ch. 2 - Prob. 2.8PCh. 2 - Prob. 2.9PCh. 2 - Prob. 2.10P
Ch. 2 - Prob. 2.11PCh. 2 - Obtain the inverse Laplace transform xt for each...Ch. 2 - Solve the following problems: 5x=7tx0=3...Ch. 2 - Solve the following: 5x+7x=0x0=4 5x+7x=15x0=0...Ch. 2 - Solve the following problems: x+10x+21x=0x0=4x0=3...Ch. 2 - Solve the following problems: x+7x+10x=20x0=5x0=3...Ch. 2 - Solve the following problems: 3x+30x+63x=5x0=x0=0...Ch. 2 - Solve the following problems where x0=x0=0 ....Ch. 2 - Invert the following transforms: 6ss+5 4s+3s+8...Ch. 2 - Invert the following transforms: 3s+2s2s+10...Ch. 2 - Prob. 2.21PCh. 2 - Compare the LCD method with equation (2.4.4) for...Ch. 2 - Prob. 2.23PCh. 2 - Prob. 2.24PCh. 2 - (a) Prove that the second-order system whose...Ch. 2 - For each of the following models, compute the time...Ch. 2 - Prob. 2.27PCh. 2 - Prob. 2.28PCh. 2 - Prob. 2.29PCh. 2 - If applicable, compute , , n , and d for the...Ch. 2 - Prob. 2.31PCh. 2 - For each of the following equations, determine the...Ch. 2 - Prob. 2.33PCh. 2 - Obtain the transfer functions Xs/Fs and Ys/Fs for...Ch. 2 - a. Obtain the transfer functions Xs/Fs and Ys/Fs...Ch. 2 - Prob. 2.36PCh. 2 - Solve the following problems for xt . Compare the...Ch. 2 - Prob. 2.38PCh. 2 - Prob. 2.39PCh. 2 - Prob. 2.40PCh. 2 - Determine the general form of the solution of the...Ch. 2 - a. Use the Laplace transform to obtain the form of...Ch. 2 - Prob. 2.43PCh. 2 - Prob. 2.44PCh. 2 - Obtain the inverse transform in the form xt=Asint+...Ch. 2 - Use the Laplace transform to solve the following...Ch. 2 - Express the oscillatory part of the solution of...Ch. 2 - Prob. 2.48PCh. 2 - Prob. 2.49PCh. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - Prob. 2.52PCh. 2 - Prob. 2.53PCh. 2 - 2.54 The Taylor series expansion for tan t...Ch. 2 - 2.55 Derive the initial value theorem:
Ch. 2 - Prob. 2.56PCh. 2 - Prob. 2.57PCh. 2 - Use MATLAB to obtain the inverse transform of the...Ch. 2 - Use MATLAB to obtain the inverse transform of the...Ch. 2 - Use MATLAB to solve for and plot the unit-step...Ch. 2 - Use MATLAB to solve for and plot the unit-impulse...Ch. 2 - Use MATLAB to solve for and plot the impulse...Ch. 2 - Use MATLAB to solve for and plot the response of...
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